We got the mailing address after 2-3 days.
(You are in "reception" until then, you don't want the Army to try and forward your mail- it will get to you after you're done with basic and at AIT.. )
ANYONE can come to graduation. You'll get the info you need later on from the Drill Sgts.
IF you are going to AIT somewhere close to where you go to Basic Training your family can stick around and even drive you to AIT. (ie you could drive it in 6hrs or less.) If you're coming to Ft Gordon, you can even stay with the family (at a hotel) from Friday thru Sunday.
Good luck- follow instructions, work hard, don't make your battle buddies mad, and you'll find it a rewarding time.